A regular hexagonal pyramid has a base area of 166.28 square feet, a slant height of 9.8 feet, and a surface area of 401.48 square feet. Find the side length of the base

  8 feet

Step-by-step explanation:

The area (A) of a regular hexagon in terms of its side length (s) is ...

  A = (3√3)/2·s^2

Then the side length in terms of the area is ...

  s = √(2A/(3√3))

For the given base area, the side length is ...

  s = √(2(166.28)/(3√3)) ≈ √64.001 ≈ 8.000 . . . . feet

__

To confirm this, we can look a the side length that will give the lateral area we have. The lateral area is the difference between the total area and the base area, so is ...

  LA = 401.48 -166.28 = 235.20 . . . . square feet

In terms of slant height (h) and side length (s), this area is ...

  LA = 3sh

  s = LA/(3h) = (235.20 ft^2)/(3·9.8 ft) = 8 ft

Either way we compute it, we find the side length of the base to be 8 feet.